Plans for a crackdown on inflated motor insurance costs which would see an estimated £20 being shaved off the cost of a typical driver's policy have been unveiled by the competition watchdog.

The Competition and Markets Authority (CMA) is proposing to cap the cost of providing a courtesy car following an accident after finding there is often "little or no incentive" to keep expenses down.

Replacement vehicles collectively cost consumers between £70 million and £180 million a year through higher premiums, the CMA found.

AA Insurance estimates from the CMA's findings that, if they are put into place, the recommendations could potentially wipe around another £20 off the cost of the average motor insurance premium.

Premiums have already been tumbling in recent months amid wider Government moves to weed out bogus personal injury claims which have ramped up the cost of motor insurance generally.

According to an index run by AA Insurance, the average quoted premium for someone who shops around has already fallen by more than £100 over the last 12 months, to reach £531.

The CMA is also proposing that competition in the £11 billion private motor insurance market should be boosted by banning "price parity" agreements between comparison websites and insurers which block insurers from making their products available to consumers more cheaply elsewhere.

It said consumers should also be given clearer information about their rights following a motor accident and better explanations about the costs and benefits of taking out protection against their no claims bonus.

The CMA also recommends that City regulator the Financial Conduct Authority (FCA) looks at how insurers communicate with consumers about add-on products related to private motor insurance after finding it can be hard for people to work out the best-value add-on products in the market.

The cost of providing a courtesy car can be inflated after an accident because often, while it is the insurer of the innocent party in a car accident which arranges for their car to be temporarily replaced and repaired, it is the insurer of the driver deemed to have caused the accident which picks up the tab.

This divide between who organises the courtesy car and who pays for it results in a lack of incentives to keep costs down. Although the inflated cost is initially felt by the insurer of the driver who is at fault, it eventually feeds into everyone's premiums.

While the exact details of the level of cap on the cost of courtesy cars are still being considered, the CMA is broadly proposing that there should be a lower cap for at-fault insurers which accept liability within a short period, and a higher cap for at-fault insurers which take longer to accept liability.

The higher cap could be set at around double the level of the lower cap, which could also give insurers an incentive to sort out the issue of liability more quickly.

The CMA, which superseded the Competition Commission earlier this year, will consult on the plans before publishing a final decision in September.

The proposals received broad backing from insurers - and from brokers, who are hopeful that the moves will help them to offer some cheaper insurance deals than those appearing on comparison websites.

Simon Douglas, director of AA Insurance, said: "The CMA's recommendations could, it's estimated, wipe perhaps a further £20 or so off the average premium."

James Dalton, head of motor insurance at the Association of British Insurers (ABI), said the moves will help reduce the "often inflated bills" from credit hire operators and should help lower premiums.

Steve Maddock, managing director of claims at Direct Line Group, said the body is "delighted" with the proposals, which should help enable a " level playing field across the insurance market, which will benefit our customers and consumers more broadly".

And Andy Watson, chief executive of Ageas UK said: " Eradicating all unnecessary cost, coupled with better information for consumers to help them make informed purchasing decisions, is a good thing."

Graeme Trudgill, executive director at British Insurance Brokers' Association (Biba), described the proposals as "well-balanced".

He said: "If a customer walks into a broker's office, we believe they should be able to offer the premium at a cheaper price than on a comparison site which typically charges around £40 to £50 per lead."

Alasdair Smith, chairman of the private motor insurance investigation group and CMA deputy panel chairman, said: "There are over 25 million privately registered cars in the UK and we think these changes will benefit motorists who are currently paying higher premiums as a result of the problems we've found.

"A cap on replacement vehicle costs will reduce the amounts charged to insurers of at-fault drivers, which will cut out some of the inefficiencies in the system and feed through to reduced premiums for all drivers.

"Through the measures we propose to introduce, we will address the problems that stem from those managing the non-fault accident claim having little or no incentive to keep costs down."

Mr Smith said comparison websites are "great" in helping motorists look for the best deal, which in turn has boosted competition.

But he added: "We want to see an end to clauses which restrict an insurer's ability to price its products differently, whether on different price comparison sites or on other channels."